What must be the length and the diameter of this wire?

Question

Suppose you wish to fabricate a uniform wire from a mass m of a metal with density Pm and resistivity p. If the wire is to have a resistance of R and all the metal is to be used, what must be 

a)the length 

b) the diameter 

of the wire. 

Answer 1

Hi Dalia,

          We want to have m=ρ_mπr²L where r=radius of the wire diameter =2r, L=the length of the wire. This provides one equation which says we use all the mass to make the wire. The second equation is R= ρL/A where A is the area of the wire i.e. A=πr² . So now we have 2 equations and 2 unknowns L, and r and D =2r you should be able to solve for L and D in terms of m, ρ_m, and ρ.

 

Hope this helps.

Jim